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605-655 (Medium)|   Algebra|      
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Bunuel
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If a + 3b + 4c = 9 and a + 4b + 6c = 15, then what is the value of a + 17 Sep 2017, 03:48
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45% (medium)

Question Stats:

74% (02:12) correct 26% (02:47) wrong based on 338 sessions

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If a + 3b + 4c = 9 and a + 4b + 6c = 15, then what is the value of a + 2b + 2c?

A. 0
B. 3
C. 6
D. 9
E. 24
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B
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If a + 3b + 4c = 9 and a + 4b + 6c = 15, then what is the value of a + 17 Sep 2017, 06:30
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Given data:
a + 3b + 4c = 9
a + 4b + 6c = 15

Since a + 3b + 4c = 9, 2(a + 3b + 4c) = 18 => 2a + 6b + 8c = 18 ->(1)
It has been given that a + 4b + 6c = 15 ->(2)

(1) - (2) => a + 2b + 2c = 3(Option B)
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If a + 3b + 4c = 9 and a + 4b + 6c = 15, then what is the value of a + 17 Sep 2017, 07:02
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Bunuel
If a + 3b + 4c = 9 and a + 4b + 6c = 15, then what is the value of a + 2b + 2c?

A. 0
B. 3
C. 6
D. 9
E. 24
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a+3b+4c=9 --(1)
a+4b+6c=15 --(2)

(2)-(1) ==>a+b+2c=6--(3)

(1)-(3) ==> a+2b+2c =3

Ans:B
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If a + 3b + 4c = 9 and a + 4b + 6c = 15, then what is the value of a + 26 Feb 2020, 08:44
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Bunuel
If a + 3b + 4c = 9 and a + 4b + 6c = 15, then what is the value of a + 2b + 2c?

A. 0
B. 3
C. 6
D. 9
E. 24
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a + 3b + 4c = 9
a + 4b + 6c = 15
b+2c=6, b=6-2c

a+2b+2c=9-b-2c=9-(6-2c)-2c=9-6=3

Ans (B)
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If a + 3b + 4c = 9 and a + 4b + 6c = 15, then what is the value of a + 29 Feb 2020, 08:42
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Bunuel
If a + 3b + 4c = 9 and a + 4b + 6c = 15, then what is the value of a + 2b + 2c?

A. 0
B. 3
C. 6
D. 9
E. 24
Show more

Multiplying the first equation by 2, we have:

2a + 6b + 8c = 18

Subtracting the 2nd equation from what we have above, we are left with:

a + 2b + 2c = 3

Answer: B
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If a + 3b + 4c = 9 and a + 4b + 6c = 15, then what is the value of a + 29 Feb 2020, 11:05
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Bunuel
If a + 3b + 4c = 9 and a + 4b + 6c = 15, then what is the value of a + 2b + 2c?

A. 0
B. 3
C. 6
D. 9
E. 24
Show more
\(a + 3b + 4c = 9\)

Or, 2a + 6b + 8c = 18 ( Multiplying by 2 on both sides)

Now, \(( 2a + 6b + 8c ) - ( a + 4b + 6c ) = a + 2b + 2c\)

Or, \(a + 2b + 2c = 18 - 15\)

Or, \(a + 2b + 2c = 3\), Answer must be (B)
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If a + 3b + 4c = 9 and a + 4b + 6c = 15, then what is the value of a + 01 Mar 2020, 21:46
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Bunuel
If a + 3b + 4c = 9 and a + 4b + 6c = 15, then what is the value of a + 2b + 2c?

A. 0
B. 3
C. 6
D. 9
E. 24
Show more

From a + 4b + 6c = 15 we know that a must be an odd integer. And since 2b + 2c = even, that means a + 2b + 2c = odd. This eliminates the even options A, C and E, leaving us with B, D.
Now we see option D is the same value (9) as equation a + 3b + 4c. Since, 3b + 4c can never be the same as 2b + 2c, this leaves us with option B only.
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If a + 3b + 4c = 9 and a + 4b + 6c = 15, then what is the value of a + 27 Oct 2025, 22:54
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